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ϵ-Nash mean-field games for linear-quadratic systems with random jumps and applications

ϵ-Nash mean-field games for linear-quadratic systems with random jumps and applications This paper studies linear-quadratic-Gaussian (LQG) games of stochastic large population system with jump-diffusion processes. The most distinguishing feature, compared with the well-studied mean-field LQG games, is that the game system follows linear SDEs driven by random jumps. The individual agents of large population system are coupled both in their state dynamics and in their individual cost functionals. Each agent in large population system has negligible impact on others, but their collective behaviors will impose some significant impact on all agents. The so-called NCE methodology is introduced to deal with the dimensionality difficulty. This methodology derives a set of decentralized strategies, which is an ϵ-Nash equilibrium for a finite N population system where . A numerical example is provided to illustrate the consistency of the mean field estimation and the impact of the population's collective behaviors. As applications, a pricing problem is studied and the decentralized suboptimal price strategy is obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Control Taylor & Francis

ϵ-Nash mean-field games for linear-quadratic systems with random jumps and applications

International Journal of Control , Volume 94 (5): 11 – May 4, 2021

ϵ-Nash mean-field games for linear-quadratic systems with random jumps and applications

International Journal of Control , Volume 94 (5): 11 – May 4, 2021

Abstract

This paper studies linear-quadratic-Gaussian (LQG) games of stochastic large population system with jump-diffusion processes. The most distinguishing feature, compared with the well-studied mean-field LQG games, is that the game system follows linear SDEs driven by random jumps. The individual agents of large population system are coupled both in their state dynamics and in their individual cost functionals. Each agent in large population system has negligible impact on others, but their collective behaviors will impose some significant impact on all agents. The so-called NCE methodology is introduced to deal with the dimensionality difficulty. This methodology derives a set of decentralized strategies, which is an ϵ-Nash equilibrium for a finite N population system where . A numerical example is provided to illustrate the consistency of the mean field estimation and the impact of the population's collective behaviors. As applications, a pricing problem is studied and the decentralized suboptimal price strategy is obtained.

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References (31)

Publisher
Taylor & Francis
Copyright
© 2019 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1366-5820
eISSN
0020-7179
DOI
10.1080/00207179.2019.1651940
Publisher site
See Article on Publisher Site

Abstract

This paper studies linear-quadratic-Gaussian (LQG) games of stochastic large population system with jump-diffusion processes. The most distinguishing feature, compared with the well-studied mean-field LQG games, is that the game system follows linear SDEs driven by random jumps. The individual agents of large population system are coupled both in their state dynamics and in their individual cost functionals. Each agent in large population system has negligible impact on others, but their collective behaviors will impose some significant impact on all agents. The so-called NCE methodology is introduced to deal with the dimensionality difficulty. This methodology derives a set of decentralized strategies, which is an ϵ-Nash equilibrium for a finite N population system where . A numerical example is provided to illustrate the consistency of the mean field estimation and the impact of the population's collective behaviors. As applications, a pricing problem is studied and the decentralized suboptimal price strategy is obtained.

Journal

International Journal of ControlTaylor & Francis

Published: May 4, 2021

Keywords: Mean-field game; large population; jump-diffusion; decentralised control; ϵ -Nash equilibrium

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